Question

For this question, why is a "µ" symbol used in the null and alternative hypothesis versus a "p"? I'm unsure if the "µ" is correct in my answer.

Excel Assignment

Samsung manufactures cellphone with an average standby time of 10 hours between charges. The standby time of the cellphone is normally distributed. During the design stage, the quality engineering staff recorded 18 observations of the standby time of the cellphone. Using the observations below, is there evidence that the average standby time of a Samsung cellphones is not 10 hours? Use a level of significance of .05

Observation

Observations	Time
1	10.85
2	11.4
3	10.81
4	10.24
5	10.23
6	9.49
7	9.89
8	10.11
9	10.57
10	11.21
11	10.1
12	11.22
13	10.31
14	11.24
15	9.51
16	10.52
17	9.92
18	8.33

Answer the following question:

1. What is the null and alternative hypothesis to the case above?

Null Hypothesis is H0: µ = 10

Alternative Hypothesis is Ha: µ ≠ 10

Answer 1

"µ" is correct in your answer.

µ =Population mean (i.e., population average) standby time.

Population is all Samsung cellphones being manufactured and the variable of interest is standby time.

So, µ =Average standby time of all Samsung cellphones being manufactured.

Null Hypothesis(H0) always has "equality" sign. So, H0 is µ = 10 hours.

Alternative Hypothesis(Ha) is exact opposite of H0. So, Ha is µ ≠ 10 hours. (It's a two-tailed test).

Alternative hypothesis is generally what we claim and we determine if there is a sufficient statistical evidence to support our claim, i.e., to support the alternative hypothesis.

Sometimes, null hypothesis may be given as a claim but we always need to use "equality" sign for null hypothesis.

"p" is the population proportion which is used in null and alternative hypotheses when we were given sample proportion, ​​​​​​. But we were given the sample mean (or sample average), and so, we use population mean, ​​​​​​.

Sample mean was given, in the sense, we need to determine it from the given sample of 18 standby times.

Here, the question is about the population average, but not about the population proportion, p.